# On the Equilibrium Shape of an Ice Crystal

Source: [On the Equilibrium Shape of an Ice Crystal](<https://www.sota2.com/research/paper/68fa2b491e209131ce845596>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T14:05:28.049Z

Authors: Kenneth G. Libbrecht

Published: 2012-05-07T16:25:16.000Z

## Abstract

We examine the shape of a an isolated, dislocation-free ice crystal when it is in equilibrium with the vapor phase in an isothermal closed environment, as a function of temperature. From our analysis we draw the following conclusions: 1) The equilibrium shape has not yet been definitively measured for ice crystals; 2) The surface energy anisotropy is likely cusp-like near the facet angles, and the size of the cusps can be estimated from crystal growth measurements; 3) The equilibrium shape is likely nearly spherical with only small faceted regions; 4) The time needed to reach equilibrium is likely prohibitively long, except under special circumstances; and 5) Surface energy effects likely play a relatively smaller role in ice crystal growth dynamics when compared to the role of attachment kinetics.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1205.1452>)

[PDF](<https://arxiv.org/pdf/1205.1452.pdf>)